The Lefschetz property, formality and blowing up in symplectic geometry

2004/03/31 by Gil R. Cavalcanti
Mathematics · #math.SG #math.DG #msc:53D35 #msc:57R19

paper · pdf

published as Trans. Amer. Math. Soc. 359 (2007), 333--348. · 19 pages. Minor changes in the text, typos corrected. To appear in Trans. Amer. Math. Soc

arxiv created 2005/04/06 · arxiv updated 2009/12/01

Abstract

In this paper we study the behaviour of the Lefschetz property under the blow-up construction. We show that it is possible to reduce the dimension of the kernel of the Lefschetz map if we blow up along a suitable submanifold satisfying the Lefschetz property. We use that, together with results about Massey products, to construct nonformal (simply connected) symplectic manifolds satisfying the Lefschetz property.

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• Symplectic non-Kähler manifolds with and without the Hard Lefschetz Condition